RUINING THINGS FOR YOU BECAUSE I AM A PETTY, PETTY MAN...

Pick a number, double it, add 10, divide it by 2, then minus it by the number you started with. You got 5.

     Saw that on a Twitter post earlier today. Okay, Twitter limits your posts to a maximum of 140 characters so I'll forgive the improper use of math terms and grammar but what remains is not at all amazing. Have you ever broken it down before or were you content with the mathematical slight-of-hand? Taken in steps, it looks like this:

Pick any number:
Okay, let's go with a variable instead so that we may represent all numbers and not just integers including (but not necessarily limited to) fractions, decimals, irrational, and imaginary numbers. I choose the old standby n.

Double that number:
2n

Add 10 to that product:
2n + 10

Divide that sum by 2:
(2n + 10) / 2

Subtract from that quotient, your original number:
[(2n + 10) / 2] - n

The difference will be 5:
Wow! Amazing!

However, let's break it down as we go this time:

Pick any number:
n

Double that number:
2n

Add 10 to that product:
2n + 10
Take note that this is the last step given to the participant which cannot be simplified.

Divide that sum by 2:
(2n + 10) / 2
simplify:
(2n / 2) + (10 / 2)
n + 5
The purpose of the Step Four is to undo Step Two. With the appearance of the number 5, the step also reveals that to control this equation for any result, simply double whatever you desire to be the outcome. In other words, had you wanted 7 to be the resultant difference, you would require the participant to add 14 to their (now doubled) original number.

Subtract from that quotient, your original number:
(n + 5) - n
simplify:
5
The purpose of the Step Five is to undo Step One. You know, the one thing you actually did that the host could not anticipate. But had he done this right away, you would have caught on so, through the flourish of busywork, the host has successfully distracted you from this exercise's preordained conclusion, bestowing upon him the suggestion of clairvoyance provided that you, the participant, choose not to reflect upon it too deeply (or at all). One might also think of this exercise as an intelligence test of sorts based on how it is repeated to others. Did you change the addend in Step Three, or leave it at 10? Did you suggest tripling or halving the original number (and yours as well) in Step Two, or did you leave it at doubling? I'm sure you can think of many other ways one might manipulate this equation ;-)

The difference will be 5:
Not so amazing this time around, right? Now take this knowledge and have some fun with your friends!